Three-Dimensional MHD Casson Fluid Flow with Couple Stress and Nanofluid Heat Transfer: A Numerical Study

Abstract

This study examines the three-dimensional, incompressible, laminar magnetohydrodynamic (MHD) flow of couple stress nanofluids over a porous, linearly stretching sheet, incorporating Brownian motion and thermophoresis phenomena. The governing nonlinear partial differential equations are transformed into ordinary differential equations through similarity variables and numerically solved using MATLAB’s bvp4c solver. Critical parameters—including the Casson fluid parameter, magnetic field strength, porosity, and thermal diffusion coefficients—are evaluated to determine their impact on velocity profiles, temperature distribution, and nanoparticle concentration. Graphical and tabular data illustrate changes in boundary layer dynamics, skin friction, and heat and mass transfer rates. The findings are validated against existing literature, reinforcing the model’s accuracy and offering valuable insights into nanofluid transport mechanisms in porous structures subjected to magnetic effects. The analysis enhances
understanding of thermal performance and fluid dynamics in advanced engineering and energy applications, supporting future research in nanofluid-enhanced systems.